In a saucepan over medium heat, steam or boil the carrots until tender. Drain, then mash the carrots and season with salt and pepper. Preheat the oven to 350 degrees F. Grease a 1-quart casserole. In a small bowl, beat the egg yolks. In another bowl, combine the carrots, egg yolks, bread crumbs, onion, and milk. In a large, chilled bowl, beat the egg whites until stiff. Gently fold the whipped whites into the carrot mixture. Turn into the prepared casserole. Bake for 45 to 60 minutes, or until a toothpick comes out clean. Serve hot.